Parameter set estimation for nonlinear systems

In this paper, we will show how parameter set estimation (PSE) can be applied to nonlinear systems. Parameter set estimation identifies a set of estimates which are feasible with respect to the measured data and a priori information. This set of parameters, feasible for the given model structure, can then be used for system tracking or robust control designs. For application to robust control, it is important that the size of this set be as small as possible. In order to apply parameter set estimation techniques to a nonlinear system, the system function is expressed in a tensor parameterization which is linear in the parameters (LP). Then it is shown how an optimum volume ellipsoid strategy for linear time invariant systems can be extended to this tensor parameterization of a nonlinear system. The methodology is illustrated via an example which uses data obtained from an operating glass furnace